If it is market where WN flies non-stop or has a heavy presence, then yes, the legacy carriers will generally match WN's pricing and rules which do not require Saturday night stay's for the cheaper fares. However, for smaller markets have limited or no WN presence, you will still see the legacies requiring Saturday night/min stays for their cheaper fares.

Your worldview is distorted because you are based in LAX where WN has a strong presence. You will still find a number of markets where UA has Sat night/min stay requirements for cheap fares out of LAX, but they are few and far between. Some examples JXN, ASE, TEX, HSV, TYS, SGF.